Answer:
46°
Step-by-step explanation:
3)
![\begin{array}{c|c}\underline{Statement}&\underline{Reason}\\ 1.AY=BX&\text{1. Given}\\ 2.AB \cong AB&\text{2. Reflexive Property}\\ 3. AD || BC&\text{3. Property of a square}\\ 4. \angle ABE \cong \angle AXB&\text{4. Alternate Interior Angles}\\ 5. \angle BAY \cong \angle BYA&\text{5. Alternate Interior Angles}\\6. \triangle BAX \cong \triangle ABY&\text{6. Angle-Side-Angle Theorem}\\ 7. AX \cong BY&\text{7. CPCTC}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7D%5Cunderline%7BStatement%7D%26%5Cunderline%7BReason%7D%5C%5C%201.AY%3DBX%26%5Ctext%7B1.%20Given%7D%5C%5C%202.AB%20%5Ccong%20AB%26%5Ctext%7B2.%20Reflexive%20Property%7D%5C%5C%203.%20AD%20%7C%7C%20BC%26%5Ctext%7B3.%20Property%20of%20a%20square%7D%5C%5C%204.%20%5Cangle%20ABE%20%5Ccong%20%5Cangle%20AXB%26%5Ctext%7B4.%20Alternate%20Interior%20Angles%7D%5C%5C%205.%20%5Cangle%20BAY%20%5Ccong%20%5Cangle%20BYA%26%5Ctext%7B5.%20Alternate%20Interior%20Angles%7D%5C%5C6.%20%5Ctriangle%20BAX%20%5Ccong%20%5Ctriangle%20ABY%26%5Ctext%7B6.%20Angle-Side-Angle%20Theorem%7D%5C%5C%207.%20AX%20%5Ccong%20BY%26%5Ctext%7B7.%20CPCTC%7D%5C%5C%5Cend%7Barray%7D)
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6)
![\begin{array}{c|c}\underline{Statement}&\underline{Reason}\\1. AB=CF&\text{1. Given}\\2.AB+BF=A'F&\text{2. Segment Addition Postulate}\\3.CF+BF=A'F&\text{3. Substitution Property}\\4.CF+BF+BC&\text{4. Segment Addition Postulate}\\5.A'F=BC&\text{5. Transitive Property}\\6. \angle AFE = \angle DBC&\text{6. Given}\\7. EF = BD&\text{7. Given}\\8. \triangle AFE \cong \triangle CBD&\text{8. Side-Angle-Side Theorem}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7D%5Cunderline%7BStatement%7D%26%5Cunderline%7BReason%7D%5C%5C1.%20AB%3DCF%26%5Ctext%7B1.%20Given%7D%5C%5C2.AB%2BBF%3DA%27F%26%5Ctext%7B2.%20Segment%20Addition%20Postulate%7D%5C%5C3.CF%2BBF%3DA%27F%26%5Ctext%7B3.%20Substitution%20Property%7D%5C%5C4.CF%2BBF%2BBC%26%5Ctext%7B4.%20Segment%20Addition%20Postulate%7D%5C%5C5.A%27F%3DBC%26%5Ctext%7B5.%20Transitive%20Property%7D%5C%5C6.%20%5Cangle%20AFE%20%3D%20%5Cangle%20DBC%26%5Ctext%7B6.%20Given%7D%5C%5C7.%20EF%20%3D%20BD%26%5Ctext%7B7.%20Given%7D%5C%5C8.%20%5Ctriangle%20AFE%20%5Ccong%20%5Ctriangle%20CBD%26%5Ctext%7B8.%20Side-Angle-Side%20Theorem%7D%5C%5C%5Cend%7Barray%7D)
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7)
![\begin{array}{c|c}\underline{Statement}&\underline{Reason}\\\text{1.AC bisects }\angle BAD&\text{1. Given}\\2. \angle BAC \cong \angle DAC&\text{2. Property of angle bisector}\\3.AC = AC&\text{3. Reflexive Property}&4. \angle ACB \cong \angle ACD&\text{4. Property of angle bisector}\\5. \triangle ABC \cong \triangle ADC&\text{5. Angle-Side-Angle Theorem}\\6.BC=CD&\text{6. CPCTC}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7D%5Cunderline%7BStatement%7D%26%5Cunderline%7BReason%7D%5C%5C%5Ctext%7B1.AC%20bisects%20%7D%5Cangle%20BAD%26%5Ctext%7B1.%20Given%7D%5C%5C2.%20%5Cangle%20BAC%20%5Ccong%20%5Cangle%20DAC%26%5Ctext%7B2.%20Property%20of%20angle%20bisector%7D%5C%5C3.AC%20%3D%20AC%26%5Ctext%7B3.%20Reflexive%20Property%7D%264.%20%5Cangle%20ACB%20%5Ccong%20%5Cangle%20ACD%26%5Ctext%7B4.%20Property%20of%20angle%20bisector%7D%5C%5C5.%20%5Ctriangle%20ABC%20%5Ccong%20%5Ctriangle%20ADC%26%5Ctext%7B5.%20Angle-Side-Angle%20Theorem%7D%5C%5C6.BC%3DCD%26%5Ctext%7B6.%20CPCTC%7D%5C%5C%5Cend%7Barray%7D)
Answer:
-1.25
Step-by-step explanation:
Your points one the graph are (-4,4) and (0,-1)
Formula for slope is y1-y2/x1-x2
4--1/-4-0
5/-4
-1.25
She has 65 water bottles....and she is buying boxes of water bottles (x) that hold 16 water bottles each. She can only buy up to 5 water bottles.
f(x) = 16x + 65...where f(x) = total water bottles and x = number of boxes
x < = 5.....here is ur restriction
the range is ur f(x) values which represent the total number of water bottles...keep in mind, she can only buy 5. Therefore, the numbers that can be subbing in for x are 0 thru 5.
So when subbing in 0 thru 5 for x, the results for f(x) are :
{ 65,81,97,113,129 } <== ur range
Answer:
The closed linear form of the given sequence is ![a_{n}=0.75n-0.45](https://tex.z-dn.net/?f=a_%7Bn%7D%3D0.75n-0.45)
Step-by-step explanation:
Given that the first term
and ![a_{n+1}=a_{n}+0.75](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3Da_%7Bn%7D%2B0.75)
To find the closed linear form for the given sequence
The formula for arithmetic sequence is
(where d is the common difference)
The above equation is of the given form ![a_{n+1}=a_{n}+0.75](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3Da_%7Bn%7D%2B0.75)
Comparing this we get d=0.75
With
and d=0.75
We can substitute these values in
![=0.3+(n-1)(0.75)](https://tex.z-dn.net/?f=%3D0.3%2B%28n-1%29%280.75%29)
![=0.3+0.75n-0.75](https://tex.z-dn.net/?f=%3D0.3%2B0.75n-0.75)
![=-0.45+0.75n](https://tex.z-dn.net/?f=%3D-0.45%2B0.75n)
Rewritting as below
![=0.75n-0.45](https://tex.z-dn.net/?f=%3D0.75n-0.45)
Therefore ![a_{n}=0.75n-0.45](https://tex.z-dn.net/?f=a_%7Bn%7D%3D0.75n-0.45)
Therefore the closed linear form of the given sequence is ![a_{n}=0.75n-0.45](https://tex.z-dn.net/?f=a_%7Bn%7D%3D0.75n-0.45)